Finite Group Databasebeta

← Group #72256447

Character table — Group #72256447

Order 2048.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size1111222222444444444444888888881616161616161616161616161616161616161616161616161616161632323232323232323232323232323232323232323232646464646464646464646464
order12222222222222444444442222444422222222444444444444888888884444444444444488888888444444448888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ41111111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1
χ5111111111111111111111111111111111-1-1-1-1111111111111111111111-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ6111111111111111111111111111111111-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111
χ7111111111111111111111111111111111-1-1-1-1111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ8111111111111111111111111111111111-1-1-1-1111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-11111
χ911-1-1-1-1-111111-1-1111-1-11-1-111-1-1-1-11111-111-1-1-11-1iiii−i−i−i−i1-11111-1-1-1-111-1-11-111-1-1ii−i−iii−i−iii−i−iii−i−iii−i−i11-1-1
χ1011-1-1-1-1-111111-1-1111-1-11-1-111-1-1-1-11111-111-1-1-11-1iiii−i−i−i−i1-1-1-1-1-1111111-1-11-1-1-111−i−iiiii−i−i−i−iiiii−i−i−i−iii-1-111
χ1111-1-1-1-1-111111-1-1111-1-11-1-111-1-1-1-11111-111-1-1-11-1−i−i−i−iiiii1-11111-1-1-1-111-1-11-111-1-1−i−iii−i−iii−i−iii−i−iii−i−iii11-1-1
χ1211-1-1-1-1-111111-1-1111-1-11-1-111-1-1-1-11111-111-1-1-11-1−i−i−i−iiiii1-1-1-1-1-1111111-1-11-1-1-111ii−i−i−i−iiiii−i−i−i−iiiii−i−i-1-111
χ1311-1-1-1-1-111111-1-1111-1-11-1-111-1-1-1-11111-1-1-111-11-1iiii−i−i−i−i1-11111-1-1-1-1-1-111-1111-1-1ii−i−iii−i−iii−i−i−i−iii−i−iii-1-111
χ1411-1-1-1-1-111111-1-1111-1-11-1-111-1-1-1-11111-1-1-111-11-1iiii−i−i−i−i1-1-1-1-1-11111-1-111-11-1-111−i−iiiii−i−i−i−iii−i−iiiii−i−i11-1-1
χ1511-1-1-1-1-111111-1-1111-1-11-1-111-1-1-1-11111-1-1-111-11-1−i−i−i−iiiii1-11111-1-1-1-1-1-111-1111-1-1−i−iii−i−iii−i−iiiii−i−iii−i−i-1-111
χ1611-1-1-1-1-111111-1-1111-1-11-1-111-1-1-1-11111-1-1-111-11-1−i−i−i−iiiii1-1-1-1-1-11111-1-111-11-1-111ii−i−i−i−iiiii−i−iii−i−i−i−iii11-1-1
χ1722222222222222222222222222-2-2-2-2-2-2-20000-22222222222-2-20000000000000000000000-2-2-2-20000000000000000
χ1822222222222222222222222222-2-2-2-2-2-2-20000-222-2-2-2-2-2-2-2-2-2-2000000000000000000000022220000000000000000
χ192222222222222222222222-2-2-2-22222-2-2-20000-2-2-2000000002222222222000000-2-2-2-2000000000000000000000000
χ202222222222222222222222-2-2-2-22222-2-2-20000-2-2-20000000022-2-2-2-2-2-2-2-20000002222000000000000000000000000
χ212222222222222222222222-2-2-2-2-2-2-2-222200002-2-200000000-2-200000000000000000022220000-2-2-2-2000000000000
χ222222222222222222222222-2-2-2-2-2-2-2-222200002-2-200000000-2-2000000000000000000-2-2-2-200002222000000000000
χ232222222222-2-2-2-22-2-22-222-2222222222-222222-2-2-200000000-2-200000000-2-2-2-2220000000000000000000000000000
χ242222222222-2-2-2-22-2-22-222-2222222222-22-2-2-2-2-2-2-200000000-2-2000000002222-2-20000000000000000000000000000
χ252222222222-2-2-2-22-2-22-222-22222-2-2-2-2-22-200002-2-200000000220000000000000000000000000000002-22-200000000
χ262222222222-2-2-2-22-2-22-222-22222-2-2-2-2-22-200002-2-20000000022000000000000000000000000000000-22-2200000000
χ272222222222-2-2-2-22-2-22-222-2-2-2-2-22222-22-2000022200000000-2-2000000000000000000000000000000000000002-22-2
χ282222222222-2-2-2-22-2-22-222-2-2-2-2-22222-22-2000022200000000-2-200000000000000000000000000000000000000-22-22
χ292222222222-2-2-2-22-2-22-222-2-2-2-2-2-2-2-2-22-220000-222000000002200000000000000000000000000000000002i−2i2i−2i0000
χ302222222222-2-2-2-22-2-22-222-2-2-2-2-2-2-2-2-22-220000-22200000000220000000000000000000000000000000000−2i2i−2i2i0000
χ3122-2-2-2-2-222222-2-2222-2-22-2-222-2-222-2-2-2-22000022-22i2i2i2i−2i−2i−2i−2i-220000000000000000000000−2i−2i2i2i0000000000000000
χ3222-2-2-2-2-222222-2-2222-2-22-2-222-2-222-2-2-2-22000022-2−2i−2i−2i−2i2i2i2i2i-2200000000000000000000002i2i−2i−2i0000000000000000
χ3322-2-2-2-2-222222-2-2222-2-22-2-2-2-22222-2-222-20000-2-2200000000-220000000000000000002i2i−2i−2i0000−2i−2i2i2i000000000000
χ3422-2-2-2-2-222222-2-2222-2-22-2-2-2-22222-2-222-20000-2-2200000000-22000000000000000000−2i−2i2i2i00002i2i−2i−2i000000000000
χ3522-2-2-2-2-222222-2-2222-2-22-2-2-2-222-2-222-2-2200002-22000000002-22222-2-2-2-2000000-2-222000000000000000000000000
χ3622-2-2-2-2-222222-2-2222-2-22-2-2-2-222-2-222-2-2200002-22000000002-2-2-2-2-2222200000022-2-2000000000000000000000000
χ3722-2-2-2-2-2222-2-2222-2-2-222-2222-2-222-2-2-2220000-2-22000000002-20000000000000000000000000000002i−2i−2i2i00000000
χ3822-2-2-2-2-2222-2-2222-2-2-222-2222-2-222-2-2-2220000-2-22000000002-2000000000000000000000000000000−2i2i2i−2i00000000
χ3922-2-2-2-2-2222-2-2222-2-2-222-2222-2-2-2-2222-2-222-2-22-2200000000-2200000000-2-2222-20000000000000000000000000000
χ4022-2-2-2-2-2222-2-2222-2-2-222-2222-2-2-2-2222-2-2-2-2222-2200000000-220000000022-2-2-220000000000000000000000000000
χ4122-2-2-2-2-2222-2-2222-2-2-222-22-2-22222-2-22-2-2000022-2000000002-200000000000000000000000000000000002-2-220000
χ4222-2-2-2-2-2222-2-2222-2-2-222-22-2-22222-2-22-2-2000022-2000000002-20000000000000000000000000000000000-222-20000
χ4322-2-2-2-2-2222-2-2222-2-2-222-22-2-222-2-222-2220000-22-200000000-22000000000000000000000000000000000000002-2-22
χ4422-2-2-2-2-2222-2-2222-2-2-222-22-2-222-2-222-2220000-22-200000000-2200000000000000000000000000000000000000-222-2
χ4544444444444444-4-4-4-4-4-4-4-40000000000022220000000000000000000002-22-2-2-20000000000000000000000000000
χ4644444444444444-4-4-4-4-4-4-4-400000000000-2-2-2-2000000000000000000000-22-22220000000000000000000000000000
χ474444444444-4-4-4-4-444-44-4-44000000000002222000000000000000000000-22-22-2-20000000000000000000000000000
χ484444444444-4-4-4-4-444-44-4-4400000000000-2-2-2-20000000000000000000002-22-2220000000000000000000000000000
χ4944444-4-44-4-4000004-40400-400000000000000000022-2-222-2-2002i2i−2i−2i2i2i−2i−2i0000000000000000002i−2i2i−2i000000000000
χ5044444-4-44-4-4000004-40400-400000000000000000022-2-222-2-200−2i−2i2i2i−2i−2i2i2i000000000000000000−2i2i−2i2i000000000000
χ5144444-4-44-4-4000004-40400-4000000000000000000-2-222-2-222002i2i−2i−2i2i2i−2i−2i000000000000000000−2i2i−2i2i000000000000
χ5244444-4-44-4-4000004-40400-4000000000000000000-2-222-2-22200−2i−2i2i2i−2i−2i2i2i0000000000000000002i−2i2i−2i000000000000
χ534444-44-4-44-44-44-4000000000000000000000000002-22-22-22-2002i−2i2i−2i2i−2i2i−2i00000000002i−2i2i−2i00000000000000000000
χ544444-44-4-44-44-44-4000000000000000000000000002-22-22-22-200−2i2i−2i2i−2i2i−2i2i0000000000−2i2i−2i2i00000000000000000000
χ554444-44-4-44-44-44-400000000000000000000000000-22-22-22-22002i−2i2i−2i2i−2i2i−2i0000000000−2i2i−2i2i00000000000000000000
χ564444-44-4-44-44-44-400000000000000000000000000-22-22-22-2200−2i2i−2i2i−2i2i−2i2i00000000002i−2i2i−2i00000000000000000000
χ574444-4-44-4-440000400-40-44000004-44-400000000002-2-222-2-220000000000000000000000002-22-20000000000000000
χ584444-4-44-4-440000400-40-44000004-44-40000000000-222-2-222-2000000000000000000000000-22-220000000000000000
χ594444-4-44-4-440000400-40-4400000-44-4400000000002-2-222-2-22000000000000000000000000-22-220000000000000000
χ604444-4-44-4-440000400-40-4400000-44-440000000000-222-2-222-20000000000000000000000002-22-20000000000000000
χ614444-4-44-4-440000-400404-404-44-40000000000000000000000002-2-222-2-220000002-22-2000000000000000000000000
χ624444-4-44-4-440000-400404-404-44-4000000000000000000000000-222-2-222-2000000-22-22000000000000000000000000
χ634444-4-44-4-440000-400404-40-44-440000000000000000000000002-2-222-2-22000000-22-22000000000000000000000000
χ644444-4-44-4-440000-400404-40-44-44000000000000000000000000-222-2-222-20000002-22-2000000000000000000000000
χ6544-4-444-4-4-44000040040-4-4000004-4-4400000000002i−2i−2i2i−2i2i2i−2i000000000000000000000000−2i2i2i−2i0000000000000000
χ6644-4-444-4-4-44000040040-4-4000004-4-440000000000−2i2i2i−2i2i−2i−2i2i0000000000000000000000002i−2i−2i2i0000000000000000
χ6744-4-444-4-4-44000040040-4-400000-444-400000000002i−2i−2i2i−2i2i2i−2i0000000000000000000000002i−2i−2i2i0000000000000000
χ6844-4-444-4-4-44000040040-4-400000-444-40000000000−2i2i2i−2i2i−2i−2i2i000000000000000000000000−2i2i2i−2i0000000000000000
χ6944-4-444-4-4-440000-400-404404-4-440000000000000000000000002-2-22-222-20000002-2-22000000000000000000000000
χ7044-4-444-4-4-440000-400-404404-4-44000000000000000000000000-222-22-2-22000000-222-2000000000000000000000000
χ7144-4-444-4-4-440000-400-40440-444-40000000000000000000000002-2-22-222-2000000-222-2000000000000000000000000
χ7244-4-444-4-4-440000-400-40440-444-4000000000000000000000000-222-22-2-220000002-2-22000000000000000000000000
χ7344-4-44-44-44-44-4-44000000000000000000000000002i−2i2i−2i−2i2i−2i2i002i−2i2i−2i−2i2i−2i2i0000000000-222-200000000000000000000
χ7444-4-44-44-44-44-4-44000000000000000000000000002i−2i2i−2i−2i2i−2i2i00−2i2i−2i2i2i−2i2i−2i00000000002-2-2200000000000000000000
χ7544-4-44-44-44-44-4-4400000000000000000000000000−2i2i−2i2i2i−2i2i−2i002i−2i2i−2i−2i2i−2i2i00000000002-2-2200000000000000000000
χ7644-4-44-44-44-44-4-4400000000000000000000000000−2i2i−2i2i2i−2i2i−2i00−2i2i−2i2i2i−2i2i−2i0000000000-222-200000000000000000000
χ7744-4-4-4444-4-4000004-40-40040000000000000000002i2i−2i−2i−2i−2i2i2i002i2i−2i−2i−2i−2i2i2i000000000000000000-222-2000000000000
χ7844-4-4-4444-4-4000004-40-40040000000000000000002i2i−2i−2i−2i−2i2i2i00−2i−2i2i2i2i2i−2i−2i0000000000000000002-2-22000000000000
χ7944-4-4-4444-4-4000004-40-4004000000000000000000−2i−2i2i2i2i2i−2i−2i002i2i−2i−2i−2i−2i2i2i0000000000000000002-2-22000000000000
χ8044-4-4-4444-4-4000004-40-4004000000000000000000−2i−2i2i2i2i2i−2i−2i00−2i−2i2i2i2i2i−2i−2i000000000000000000-222-2000000000000
χ8144-4-4-4-4-444444-4-4-4-4-444-4440000000000022-2-20000000000000000000002-2-22-220000000000000000000000000000
χ8244-4-4-4-4-444444-4-4-4-4-444-44400000000000-2-222000000000000000000000-222-22-20000000000000000000000000000
χ8344-4-4-4-4-4444-4-444-4444-4-44-40000000000022-2-2000000000000000000000-222-2-220000000000000000000000000000
χ8444-4-4-4-4-4444-4-444-4444-4-44-400000000000-2-2220000000000000000000002-2-222-20000000000000000000000000000
χ8588888-8-88-8-800000-880-80080000000000000000000000000000000000000000000000000000000000000000000000
χ868888-88-8-88-8-88-88000000000000000000000000000000000000000000000000000000000000000000000000000000
χ8788-8-88-88-88-8-888-8000000000000000000000000000000000000000000000000000000000000000000000000000000
χ8888-8-8-8888-8-800000-880800-80000000000000000000000000000000000000000000000000000000000000000000000
χ8916-1616-16000000000000000000000000000004-44-40000000000000000000000000000000000000000000000000000000
χ9016-1616-1600000000000000000000000000000-44-440000000000000000000000000000000000000000000000000000000
χ9116-16-1616000000000000000000000000000004-4-440000000000000000000000000000000000000000000000000000000
χ9216-16-161600000000000000000000000000000-444-40000000000000000000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).